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You are combining the images in the form
Show[Graphics[simplePrimitives], complicatedRegionPlot]
The options in the resulting figure are inherited from the first term, namely Graphics[simplePrimitives]. This does not include the "TransparentPolygonMesh" -> True generated by RegionPlot. You see the mesh as a result. If you combine things as follows:
...

Update: With the function top defined in the original post you can replicate all the cool things you see in rm-rf's answer in the linked Q/A. For example, with a slight modification of gr1, i.e.,
Graphics3D[hexTile[20, 20] /.
Polygon[l_] :> {Directive[Orange, Opacity[0.8], Specularity[White, 30]],
Polygon[l], Polygon[{Pi/5, 0} + {-1, 1} # & ...

First, you can generate your random points like so:
SeedRandom[1];
pts = RandomReal[{0, 12}, {100, 2}];
The DelaunayTriangulation command returns an adjacency list representation of the triangulation.
Needs["ComputationalGeometry`"];
dt = DelaunayTriangulation[pts];
dt // Column
This says that the first point should be connected to the 2nd, the 24th, ...

Not sure about the creation of a "smooth" surface. But from Mma help, you may create a convex hull in 3D by using TetGenConvexHull
Needs["TetGenLink`"]
data3D = RandomReal[{0, 1}, {100, 3}];
Graphics3D[Point[data3D]];
surface = TetGenConvexHull[data3D];
(* TetGenConvexHull was changed sometime between 8.0.0 and 8.0.4.
Uncomment the following line only if ...

Here are a few additions to @RunnyKine suggestions. If you are ever in doubt about the quality of a mesh (an ElementMesh to be exact) you can query the mesh.
Needs["NDSolve`FEM`"]
region = ImplicitRegion[! (Norm[{x, y, z}] < 1), {{x, -5, 5}, {y, -5,
5}, {z, 0, 5}}];
mesh = ToElementMesh[region];
Min[mesh["Quality"]]
0.004439742441262357`
So the ...

NMinimize does not work with ElementMesh (which is not RegionQ) directly. Perhaps it could, but for now I would suggest converting the element mesh to a region:
NMinimize[x^2 + y^2, {x, y} \[Element] MeshRegion[disk]]
This will work in Mathematica 10.0.2 and later.

As pointed out in the comments, there's really no mathematical definition of a concave hull.
Of course, just because there's no mathematical definition does not preclude coming up with something that sort of works. I can think of two ways to do this:
Easy Way, Not General
Your data roughly has axial symmetry parallel to the x-axis. Moreover, all of your ...

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